The critical O(N) CFT: Methods and conformal data

Henriksson, Johan

doi:10.48550/arxiv.2201.09520

Cited by 7 publications

(38 citation statements)

References 242 publications

(526 reference statements)

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“…9 and 10 the dimensions of the subleading operators φ , t , J µ and T µν as determined by the Extremal Functional Method (EFM) [46] at each navigator minimum 4 . Most of the operators stay well above the gap assumptions made, as expected from the -expansion (here we show the unresummed expansions given in the recent review article [25] 5 ). Only t near d = 4 has a dimension close to the gap assumed, but from the top right of Fig.…”

Section: Sailing Through D: From the Perturbative To The Non-perturba...supporting

confidence: 77%

“…The fractal dimension d f ( ) is also known to 6-loops [17], while the RG dimension y 4,2 ( ) is known to only 5-loops [22]. A collection of all known -expansion CFT data was recently given in [25], and we will refer to it for data not listed in Eq. ( 2).…”

Section: Theorymentioning

confidence: 99%

“…Even though Ward identities were not imposed in (10), the navigator minima were deep enough in the allowed region that they were still allowed after imposing Ward identities. 5 T µν is compared to the second subleading operator of [25] λ ssOp[S,2,3] ≈ 0.41. We thank J. Henriksson for pointing this out.…”

Section: Sailing Through D: From the Perturbative To The Non-perturba...mentioning

confidence: 99%

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Navigating through the O(N) archipelago

Sirois¹

2022

Preprint

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A novel method for finding allowed regions in the space of CFT-data, coined navigator method, was recently proposed in [1]. Its efficacy was demonstrated in the simplest example possible, i.e. that of the mixed-correlator study of the 3D Ising Model. In this paper, we would like to show that the navigator method may also be applied to the study of the family of d-dimensional O(N ) models. We will aim to follow these models in the (d, N ) plane. We will see that the "sailing" from island to island can be understood in the context of the navigator as a parametric optimization problem, and we will exploit this fact to implement a simple and effective path-following algorithm. By sailing with the navigator through the (d, N ) plane, we will provide estimates of the scaling dimensions (∆ φ , ∆ s , ∆ t ) in the entire range (d, N ) ∈ [3, 4] × [1, 3]. We will show that to our level of precision, we cannot see the non-unitary nature of the O(N ) models due to the fractional values of d [2] or N [3] in this range. We will also study the limit N − → 1, and see that we cannot find any solution to the unitary mixed-correlator crossing equations below N = 1.

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Section: Sailing Through D: From the Perturbative To The Non-perturba...supporting

confidence: 77%

Section: Theorymentioning

confidence: 99%

Section: Sailing Through D: From the Perturbative To The Non-perturba...mentioning

confidence: 99%

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Navigating through the O(N) archipelago

Sirois¹

2022

Preprint

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“…Maximizing/minimizing various parameters in the approximate navigator function, we obtain the data in Table 1 25 . We found all the error bars are compatible with the data in [13] For various setups in this paper, the estimated errors ∆ σ,max − ∆ σ,min , ∆ ,max − ∆ ,min and the total error 6 i=1 (x i,max − x i,min ) is presented in Table 2 26 .…”

Section: A Preliminary Attempt On Estimation Of the Error Barmentioning

confidence: 99%

“…We thank Johan Henriksson for pointing out this fact and sharing some results of their ongoing work[24] 8 However according to[25], [σT ] shouldn't exist for < 6 in the 4 − expansion.…”

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confidence: 99%

The Hybrid Bootstrap

Su¹

2022

Preprint

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Finding a method to combine the numerical bootstrap with the analytic lightcone bootstrap is an important goal to advance the conformal bootstrap program. We propose a hybrid bootstrap method to do just that. The numerical and analytic bootstrap approaches are sensitive to different regions of the spectrum and complement each other. When they are effectively combined, the hybrid bootstrap enjoys the best of both worlds and the prediction for the actual CFT can be significantly improved. In this work, we discuss the general strategy to perform such a hybrid bootstrap, and we make a partial implementation of the strategy for 3D Ising CFT {σ, } system. Even at relatively low derivative order Λ = 19, the hybrid bootstrap predicts very precise values for the scaling dimension ∆ σ , ∆ that are within the previous Λ = 43 rigorous error bars.

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Spin impurities, Wilson lines and semiclassics

Cuomo

Komargodski

Raviv-Moshe

2022

J. High Energ. Phys.

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We consider line defects with large quantum numbers in conformal field theories. First, we consider spin impurities, both for a free scalar triplet and in the Wilson-Fisher O(3) model. For the free scalar triplet, we find a rich phase diagram that includes a perturbative fixed point, a new nonperturbative fixed point, and runaway regimes. To obtain these results, we develop a new semiclassical approach. For the Wilson-Fisher model, we propose an alternative description, which becomes weakly coupled in the large spin limit. This allows us to chart the phase diagram and obtain numerous rigorous predictions for large spin impurities in 2 + 1 dimensional magnets. Finally, we also study 1/2-BPS Wilson lines in large representations of the gauge group in rank-1 $$ \mathcal{N} $$ N = 2 superconformal field theories. We contrast the results with the qualitative behavior of large spin impurities in magnets.

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The critical O(N) CFT: Methods and conformal data

Cited by 7 publications

References 242 publications

Navigating through the O(N) archipelago

Navigating through the O(N) archipelago

The Hybrid Bootstrap

Spin impurities, Wilson lines and semiclassics

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